maths @ form 4

教學 :

看到大家的指數都不相同嗎?

這樣很頭痛吧

其實這是欺騙感情的數學

3^(x+1) , 看來跟9^x 沒有關係

其實根據指數定律, 3^(x+1)= 3^x * 3 , 即是有3個3乘以x的次方

(1)

9^x - 7 * 3^(x+1) + 108 = 0

9^x - 7 * 3^x * 3 + 108= 0

9^x - 21 * 3^x + 108= 0

(3^2) ^x - 21 * 3^x + 108= 0

3^2x - 21 * 3^x + 108= 0

108 = 9 * 12

用交叉相乘則得出(3^x-12)(3^x-9)=0

由於a^m*a^n=a^(n+m)

所以3^2x=3^x * 3^x

(3^x-12)(3^x-9)=0

3^x=9
x=2

3^x-12
3^x=12
x log 3 = log 12
x= log12/log3

x=2 or x= log12/log3
(2)

4^(x+1) - 2^(x+2) +1 = 0

這條數又在欺騙感情=3=

4^(x+1) = 4 * 4^x = 4 * (2^2) ^x = 4 *2^2x=4*2^x*2^x

2^(x+2) = 4 * 2^x

+1, 制作了-2, 肯定是-1 * -1

4*2^x*2^x- 4 * 2^x + 1 = 0

(2 * 2^x )(2 * 2^x ) = 4*2^x*2^x = 4*2^2x

直式如下
(2 * 2^x )(-1)
(2 * 2^x ) (-1)

[(2 * 2^x ) (-1)]^2=0
(2 * 2^x ) (-1)=0
2^x=1/2
2^x=2^-1
x=-1

2008-08-14 21:30:40 補充：
別人在寫指數啊

(1) 9x - 7(3x+1) + 108 = 0

Answer:
9x - 7(3x+1) + 108 = 0
9x- 21x- 7+108 = 0
-12x = -101
x= 101/12
x= 8 and 5/12

(2) 4x+1 - 2x+2 +1 = 0

Answer:
4x+1 - 2x+2 +1 = 0
2x+4 = 0
2x = -4
x = -2

1)

9x - 7(3x+1) + 108 = 0
9x - 21x - 7=108
-12x=115
x=115/-12
=-9.58 (cor. to 3 sig. fig.)

2)
4x+1-2x+2+1 = 0
2x+4 = 0
2x = -4
x = -2